SAN FRANCISCO — Nets general manager Billy King confirmed Thursday afternoon the Nets have worked out free agent center Jason Collins, and he could potentially be signed by the team to fill its need for a reliable defensive presence in the paint.

“We’re going to look at anybody that’s a free agent that’s big that’s out there,” King said on a conference call with reporters following Thursday’s trade deadline. “We’re going to look at anybody that’s in the D-League that’s big, we’re going to look at anybody coming back from China. We’ll explore all of them.

“Jason Collins is a free agent and he’s out there, so obviously he’ll be included in the list.”

Collins, who famously came out in an article in Sports Illustrated last May and would be the first openly gay athlete to compete in one the four major professional American sports, hasn’t been signed by anyone this season, and has been staying in shape in California, where the Nets worked him out recently.

“During the [All-Star Break] I was back East, so I didn’t work him out,” King said. “He’s in shape.”

Signing Collins, who turned 35 in December, would obviously be a watershed moment in American sports, and would come on the heels of former Missouri defensive end Michael Sam coming out in a series of media interviews a couple of weeks ago ahead.

But King said if the Nets choose to sign Collins, who also is reportedly drawing interest from the Clippers, it wouldn’t be for the publicity or marketing potential that would come with such a decision. It would instead hinge on whether Collins would be able to help them on the court.

“We’re going to bring in a basketball player,” he said. “It’s not about marketing or anything like that. If we’re bringing somebody in, we’re bringing them in because we feel they can help our basketball team.

“It’s not about marketing. We’re beyond doing something for gimmicks. We’re trying to get a guy to play basketball and help us win. That’s not my focus on any of that.”

The Nets were quiet on deadline day, after making their second trade in the last few weeks Wednesday by sending Jason Terry and Reggie Evans to the Kings for shooting guard Marcus Thornton. King acknowledged the Nets had pursued some other trades possibilities to secure another big man using the Disabled Player Exception they received when Brook Lopez was lost for the season. The most talked about name belonged to Lakers forward Jordan Hill, but no deal was reached.

“We were looking to add another big, and we explored numerous options with numerous teams, but we just couldn’t make a deal,” King said.

That’s where Collins could potentially fit. There are plenty of connections between Collins and the Nets that could make a potential pairing a possibility.

First, and most obvious, is the relationship between Collins and Nets coach Jason Kidd, who spent 6 ¹/₂ seasons together as Nets teammates, including the back-to-back trips to the Finals in 2002 and ’03.

“Jason’s a good friend of mine and he was also a teammate in Jersey,” Kidd said last spring after Collins made his announcement. “He’s a true professional on and off the court. It takes a lot of courage what he did, but it’s just going to make the world a better place.’’

Collins also spent three seasons playing with Joe Johnson in Atlanta. He was also a teammate of Paul Pierce and Kevin Garnett in Boston last year.

He also played for Clippers coach and senior vice president of basketball operations Doc Rivers with the Celtics, and Rivers, like Kidd, hasn’t been shy about his admiration for Collins.

“I wasn’t surprised by the article or the statement because we’d talked about it recently,’’ Rivers said in May. “He told me he was coming out and I told him, ‘Great. Good. Let’s move forward.’ And I jokingly said ‘I wish you could’ve got me more rebounds, because that’s all I care about, really.’”

There also is a relationship between the Nets and superagent Arn Tellem, who represents Collins. Tellem’s firm represents both Johnson and Lopez.